Diamond
The diamond lattice gets its strength from the intricate interconnectedness of its basic carbon atoms. This model of the elementary lattice cell shows how each (yellow or green) carbon atom is connected (in red) to 4 other atoms, in a manner that makes an atom a part of 12 hexagons, in 4 planes. The usual depiction avoids Geomag (this from Diamonds glitter): Construction (This one is a bit hard to make, you might try your hand at the smaller version below first, to get experience with the geometry.) #First make the atoms as icosahedra. In the full lattice, each isosahedron will get connections in tetrahedral directions to 4 other atoms. In this cell, this is true for the green atoms only. #Connect 4 yellow icosahedra to a central green icosahedron, to get a tetrahedral 'star'. Ultimately, there will be four such stars starting from 4 green atoms, but they overlap in their yellow parts. #Therefore it is easier to use the green star center and two of the yellow points of the star, adding two more green and one yellow, to make a hexagon of 6 atoms. You will find that the atoms are alternating in 2 planes (green and yellow), the hexagon is a bit 'wavy'. The tetrahedral nature of the connections is the clue to get this right. #Now from this hexagon expand in the other directions, constructing more hexagons (in four planes), and finishing with tetrahedral stars from the green atoms. Follow the schematic picture, and the lattice cell will take shape. #To finish the delineation of the cell, make the 24 blue rods, and affix the yellow corner icosahedra on them. Because you fix the 6 degrees of freedom of the corners, they will magically float in space. The magic is the near miss that allows the blue rods to be within about 0.5% of the true value. Alternative Views Image:Diamond_large_a.JPG|General view Image:Diamond_large_e.JPG|Sidelong view Image:Diamond_large_c.JPG|Planes of atoms Image:Diamond_large_d.JPG|Hexagonal corner view A Smaller Version of the Diamond Cell and a Nanokarat In this version, the icosahedral representation of the atoms is replaced by octahedra (this was actually my first attempt). The advantage is that it takes fewer rods to make an interesting part of the diamond lattice that begins to show the pattern beyond the elementary cell. Even though in an infinite lattice there are as many rods in the atoms as there are in the connections, a finite lattice stops at the atoms. Therefore use your most plentiful color for the atoms. #First make the atoms as octahedra. Each octahedron will get connections in tetrahedral directions to 4 other atoms. #Start making a simple hexagon out of 6 atoms, connecting the atoms in pairs. You will find that they are alternating in 2 planes, the hexagon is a bit 'wavy'. #Now from this hexagon expand in the other directions, constructing more of them, and the lattice will take shape by itself. #Stop when you run out of rods. Incidentally, the initial hexagon you have made is another example of a torus. You can use parts of the diamond lattice to make surfaces of any genus. Image:Diamond_gen_s.JPG|General view Image:Diamond_top_s.JPG|Top view Image:Diamond_side_s.JPG|Side view Image:Diamond_skew_s.JPG|Skew view Category:Polyhedron Category:Deltahedron Category:Modular Design